It has recently been proposed that the entanglement entropy can be an order parameter of confinement/deconfinement transitions. To find a clear evidence, we introduce a new quantity called the geometric entropy, which is related to the entanglement entropy via a double Wick rotation. We analyze the geometric entropy and manifestly show that its value becomes discontinuous at the Hagedorn temperature both in the free N =4 super Yang-Mills and in its supergravity dual.
N=4 Super Yang-Mills theory supplies us with a non-Abelian 4D gauge theory with a meaningful perturbation expansion, both in the UV and in the IR. We calculate the free energy on a 3-sphere and observe a deconfinement transition for large N at zero coupling. The same thermodynamic behaviour is found for a wide class of toy models, possibly also including the case of non-zero coupling. Below the transition we also find Hagedorn behaviour, which is identified with fluctuations signalling the approach to the deconfined phase. The Hagedorn and the deconfinement temperatures are identical. Applicat…
A connection between the Hagedorn transition in string theory and the deconfinement transition in (non-supersymmetric) Yang-Mills theory is made using the AdS/CFT correspondence. We modify the model of zero temperature QCD proposed by Witten by compactifying an additional space-time coordinate with supersymmetry breaking boundary conditions thus introducing a finite temperature in the boundary theory. There is a Hagedorn-like transition associated with winding modes around this coordinate, which signals a topology changing phase transition to a new AdS/Schwarzschild blackhole where this coordi…
We demonstrate that weakly coupled, large N, d-dimensional SU(N) gauge theories on a class of compact spatial manifolds (including S^{d-1} \times time) undergo deconfinement phase transitions at temperatures proportional to the inverse length scale of the manifold in question. The low temperature phase has a free energy of order one, and is characterized by a stringy (Hagedorn) growth in its density of states. The high temperature phase has a free energy of order N^2. These phases are separated either by a single first order transition that generically occurs below the Hagedorn temperature or …
We match the Hagedorn/deconfinement temperature of planar N=4 super Yang-Mills (SYM) on R x S^3 to the Hagedorn temperature of string theory on AdS_5 x S^5. The match is done in a near-critical region where both gauge theory and string theory are weakly coupled. On the gauge theory side we are taking a decoupling limit found in hep-th/0605234 in which the physics of planar N=4 SYM is given exactly by the ferromagnetic XXX_{1/2} Heisenberg spin chain. We find moreover a general relation between the Hagedorn/deconfinement temperature and the thermodynamics of the Heisenberg spin chain. On the st…
We match the Hagedorn/deconfinement temperature of planar N=4 super Yang-Mills (SYM) on R x S^3 to the Hagedorn temperature of string theory on AdS_5 x S^5. The match is done in a near-critical region where both gauge theory and string theory are weakly coupled. The near-critical region is near a point with zero temperature and critical chemical potential. On the gauge theory side we are taking a decoupling limit found in hep-th/0605234 in which the physics of planar N=4 SYM is given exactly by the ferromagnetic XXX_{1/2} Heisenberg spin chain. We find moreover a general relation between the H…
The Hagedorn transition as a Plancherel wall: Tracy-Widom statistics, Polyakov loops and partial deconfinement
School of Science, Huzhou Normal University（湖州师范学院理学院）；Mandelstam Institute for Theoretical Physics, School of Physics, University of the Witwatersrand（威特沃特斯兰德大学物理学院曼德尔斯坦理论物理研究所）；Research Institute of Basic Sciences, Seoul National University（首尔大学基础科学研究院）；Department of Physics and Astronomy & Center for Theoretical Physics, Seoul National University（首尔大学物理与天文学系及理论物理中心）
It is expected that the Gregory-Laflamme (GL) instability in the black string in gravity is related to the Rayleigh-Plateau instability in fluid mechanics. Especially, the orders of the phase transitions associated with these instabilities depend on the number of the transverse space dimensions, and they are of first and second order below and above the critical dimension. Through the gauge-gravity correspondence, the GL instability is conjectured to be thermodynamically related to the Hagedorn instability in large-N gauge theories, and it leads to a prediction that the order of the confinemen…
We use the Matrix formalism to investigate what happens to strings above the Hagedorn temperaure. We show that it is not a limiting temperature but a temperature at which the continuum string picture breaks down. We study a collection of $N$ D-0-branes arranged to form a string having $N$ units of light cone momentum. We find that at high temperatures the favoured phase is one where the string world sheet has disappeared and the low energy degrees of freedom consists of $N^2$ massless particles (``gluons''). The nature of the transition is very similar to the deconfinement transition in large-…
It has been conjectured that string theory in a pp-wave background is dual to a sector of N=4 supersymmetric Yang-Mills theory. We study the Hagedorn transition for free strings in this background. We find that the free energy at the transition point is finite suggesting a confinement/deconfinement transition in the gauge theory. In the limit of vanishing mass parameter the free energy matches that of free strings on an 8-torus with momentum/winding chemical potential. The entropy in the microcanonical ensemble with fixed energy and fixed momentum/winding is computed in each case.
We study the supergravity dual to the confinement/deconfinement phase transition for the N=4 SU(N) SYM on R x S^3 with a chemical potential conjugate to a U(1)\subset SO(6)_R charge. The appropriate supergravity system is a single charge black hole in D=5 N=8 gauged supergravity. Application of the gauge/string theory holographic renormalization approach leads to new expressions for the black hole ADM mass and its generalized free energy. We comment on the relation of this phase transition to the Hagedorn transition for strings in the maximally supersymmetric plane wave background with null RR…
We study the index of $\mathcal{N}=4$ Yang-Mills theory on $S^3\times\mathbb{R}$. We argue that the index should undergo a large $N$ deconfinement phase transition, by computing an upper bound of its `temperature.' We compute this bound by optimizing the phases of fugacities. The bound we find has some features analogous to the Hagedorn temperature. We briefly discuss a possible mechanism of the actual deconfinement transition below our bound. Our upper bound is lower than the Hawking-Page transition `temperature' of known BPS black holes in the AdS$_5$ dual. We thus expect the existence of ne…
In order to study the nuclear matter in the relativistic heavy ion collisions and the compact stars, we need the hadronic density of states for the entire ($μ_B-T$) phase transition diagram. We present a model for the continuous high-lying mass (and volume) spectrum density of states that fits the Hagedorn mass spectrum. This model explains the origin of the tri-critical point besides various phenomena such as the quarkyonic matter and the quark-gluon liquid. The Hagedorn mass spectrum is derived for the color-singlet quark-gluon bag with various internal structures such as the unimodular unit…
Following on from recent studies of string theory on a one-parameter family of integrable deformations of $AdS_{5}\times S^{5}$ proposed by Lunin and Maldacena, we carry out a systematic analysis of the high temperature properties of type IIB strings on the associated pp-wave geometries. In particular, through the computation of the thermal partition function and free energy we find that not only does the theory exhibit a Hagedorn transition in both the $(J,0,0)$ and $(J,J,J)$ class of pp-waves, but that the Hagedorn temperature is insensitive to the deformation suggesting an interesting unive…
We analyze the holographic entanglement entropy in a soliton background with Wilson lines and derive a relation analogous to the first law of thermodynamics. The confinement/deconfinement phase transition occurs due to the competition of two minimal surfaces. The entropic c function probes the confinement/deconfinement phase transition. It is sensitive to the degrees of freedom (DOF) smaller than the size of a spatial circle. When the Wilson line becomes large, the entropic c function becomes non-monotonic as a function of the size and does not satisfy the usual c-theorem. We analyze the entan…
Large $N$ gauged multi-matrix quantum mechanical models usually have a first order Hagedorn transition, related to deconfinement. In this transition the change of the energy and entropy is of order $N^2$ at the critical temperature. This paper studies the microcanonical ensemble of the model at intermediate energies $1<<E<<N^2$ in the coexistence region for the first order phase transition. Evidence is provided for a partial deconfinement phase where submatrix degrees of freedom for a $U(M)$ subgroup of $U(N)$, with $M<<N$ have an excitation energy of order $M^2$ and are effectively phase sepa…
Induced by the Hagedorn instability, weakly-coupled $U(N)$ gauge theories on a compact manifold exhibit a confinement/deconfinement phase transition in the large-$N$ limit. Recently we discover that the thermal entropy of a free theory on $\mathbb{S}^3$ gets reduced by a universal constant term, $-N^2/4$, compared to that from completely deconfined colored states. This entropy deficit is due to the persistence of Gauss's law, and actually independent of the shape of the manifold. In this paper we show that this universal term can be identified as the topological entangle entropy both in the co…
A certain sector of the matrix model for M-theory on a plane wave background has recently been shown to produce the transverse five-brane. We consider this theory at finite temperature. We find that, at a critical temperature it has a Gross-Witten phase transition which corresponds to deconfinement of the matrix model gauge theory. We interpret the phase transition as the Hagedorn transition of M-theory and of type II string theory in the five-brane background. We also show that there is no Hagedorn behaviour in the transverse membrane background case.
We calculate the equation of state of a gas of strings at high density in a large toroidal universe, and use it to determine the cosmological evolution of background metric and dilaton fields in the entire large radius Hagedorn regime, (ln S)^{1/d} << R << S^{1/d} (with S the total entropy). The pressure in this regime is not vanishing but of O(1), while the equation of state is proportional to volume, which makes our solutions significantly different from previously published approximate solutions. For example, we are able to calculate the duration of the high-density "Hagedorn" phase, which …
We consider, from several complementary perspectives, the physics of confinement and deconfinement in the 2+1 dimensional Georgi-Glashow model. Polyakov's monopole plasma and 't Hooft's vortex condensation are discussed first. We then discuss the physics of confining strings at zero temperature. We review the Hamiltonian variational approach and show how the linear confining potential arises in this framework. The second part of this review is devoted to study of the deconfining phase transition. We show that the mechanism of the transition is the restoration of 't Hooft's magnetic symmetry in…
We discuss the entropy carried by a quark-antiquark pair, in particular across the deconfinement transition. We therefore rely on a self-consistent solution to Einstein-Maxwell-dilaton gravity, capable of mimicking essential features of QCD. In particular we introduce a novel model that still captures well the QCD confinement and deconfinement phases, while allowing the introduction of a temperature in a phase which resembles the confined phase, this thanks to it being dual to a small black hole. We pay due attention to some subtleties of such model. We confirm the lattice picture of a strong …
A family of deformed black branes is employed to examine the confinement/deconfinement phase transition in AdS/QCD. The holographic entanglement entropy (HEE) plays the role of the order parameter driving the confinement/deconfinement phase transition. The binding energy of quark-antiquark bound states and the critical length that makes a null variation of the HEE, together with the critical temperature separating the deconfined quark-gluon plasma to the confined hadronic phase, are discussed in the deformed black brane background, matching current experimental hadronic data.
Banks, Fischler, Klebanov and Susskind have proposed a model for black hole thermodynamics based on the principle that the entropy is of order the number of particles at the phase transition point in a Boltzmann gas of D0-branes. We show that the deviations from Boltzmann scaling found in $d<6$ noncompact spatial dimensions have a simple explanation in the analysis of self-gravitating random walks due to Horowitz and Polchinski. In the special case of $d=4$ we find evidence for the onset of a phase transition in the Boltzmann gas analogous to the well-known Hagedorn transition in a gas of free…
Computing the entanglement entropy in confining gauge theories is often accompanied by puzzles and ambiguities. In this work we show that compactifying the theory on a small circle $\mathbb S^1_L$ evades these difficulties. In particular, we study Yang-Mills theory on $\mathbb R^3\times \mathbb S^1_L$ with double-trace deformations or adjoint fermions and hold it at temperatures near the deconfinement transition. This theory is dual to a multi-component (electric-magnetic) Coulomb gas that can be mapped either to an XY-spin model with $\mathbb Z_p$-preserving perturbations or dual Sine-Gordon …
The partition function of BFSS matrix model is studied for two different classical backgrounds upto 1-loop level. One of the backgrounds correspond to a membrane wrapped around a compact direction and another to a localized cluster of $D0$-branes. It is shown there exist phase transitions between these two configurations - but only in presence of an IR cut-off. The low temperature phase corresponds to a string (wrapped membrane) phase and so we call this the Hagedorn phase transition. While the presence of an IR cut-off seemingly is only required for perturbative analysis to be valid, the phys…
We discuss some aspects of the behaviour of a string gas at the Hagedorn temperature from a Euclidean point of view. Using AdS space as an infrared regulator, the Hagedorn tachyon can be effectively quasi-localized and its dynamics controled by a finite energetic balance. We propose that the off-shell RG flow matches to an Euclidean AdS black hole geometry in a generalization of the string/black-hole correspondence principle. The final stage of the RG flow can be interpreted semiclassically as the growth of a cool black hole in a hotter radiation bath. The end-point of the condensation is the …
We study the large N saddle points of weakly coupled N=4 super Yang-Mills theory on S^1 x S^3 that are described by a commuting matrix model for the seven scalar fields {A_0, Φ_J}. We show that at temperatures below the Hagedorn/`deconfinement' transition the joint eigenvalue distribution is S^1 x S^5. At high temperatures T >> 1/R_{S^3}, the eigenvalues form an ellipsoid with topology S^6. We show how the deconfinement transition realises the topology change S^1 x S^5 --> S^6. Furthermore, we find compelling evidence that when the temperature is increased to T = 1/(\sqrtλR_{S^3}) the saddle w…
Lattice QCD indicates a large amount of entropy associated with the heavy quark-antiquark pair immersed in the quark-gluon plasma. This entropy grows as a function of the inter-quark distance giving rise to an entropic force that can be very effective in dissociating the bound quarkonium states. In addition, the lattice data show a very sharp peak in the heavy quark-antiquark entropy at the deconfinement transition. Since the quark-gluon plasma around the deconfinement transition is strongly coupled, we employ the holographic correspondence to study the entropy associated with the heavy quark-…
In the holographic AdS/QCD approach, the confinement/deconfinement transition is associated with the Hawking-Page transition of a thermal anti-de Sitter (AdS) space to an AdS black hole. In the case of the hard wall model, the thermal transition takes place in the planar AdS thanks to the introduction of an infrared cut-off in the geometry. The corresponding thermodynamic entropy of the $SU(N) $ gauge theory jumps from proportional to $N^0$ in the confined hadronic phase to proportional to $N^2$ in the plasma phase, corresponding to the presence of the color degrees of freedom. The Hawking-Pag…
We consider a higher-dimensional hard wall model with an infrared (IR) cut-off in asymptotically AdS space and investigate its thermodynamics via the holographic renormalization method. We find a relation between the confinement temperature and the IR cut-off for any dimension. It is also shown that the entropy of $p$-branes with the number of coincident branes (the number of the gauge group) $N$ jumps from leading order in $\cal O$($N^0$) at the confining low temperature phase to $\cal O$($N^{\frac{p+1}{2}}$) at the deconfining high temperature phase like $D3$-branes ($p=3$) case. On the othe…
We employ the recent results on the generalization of the $c$-theorem to 2+1-d to derive non-perturbative results for strongly interacting quantum field theories, including QED-3 and the critical theory corresponding to certain quantum phase transitions in condensed matter systems. In particular, by demanding that the universal constant part of the entanglement entropy decreases along the renormalization group flow ("F-theorem"), we find bounds on the number of flavors of fermions required for the stability of QED-3 against chiral symmetry breaking and confinement. In this context, the exact r…
In earlier work, we introduced a dynamical Einstein--Maxwell--dilaton model which mimics essential features of QCD (thermodynamics) below and above deconfinement. Although there are some subtle differences in the confining regime of our model as compared to the standard results, we do have a temperature dependent dual metric below $T_c$ as well, allowing for a richer and more realistic holographic modeling of the QCD phase structure. We now discuss how these features leave their imprints on the associated entanglement entropy when a strip region is introduced in the various phases. We uncover …
The entropy of entanglement between a three-dimensional slab of thickness l and its complement is studied numerically for four-dimensional SU(2) lattice gauge theory. We find a signature of a nonanalytic behavior of the entanglement entropy, which was predicted recently for large N_c confining gauge theories in the framework of AdS/CFT correspondence. The derivative of the entanglement entropy over l is likely to have a discontinuity at some l = l_c. It is argued that such behavior persists even at finite temperatures, probably turning into a sort of crossover for temperatures larger than the …
We discuss a general five-dimensional completely anisotropic holographic model with three different spatial scale factors, characterized by a Van der Waals-like phase transition between small and large black holes. A peculiar feature of the model is the relation between anisotropy of the background and anisotropy of the colliding heavy ions geometry. We calculate the holographic entanglement entropy (HEE) of the slab-shaped region, the orientation of which relatively to the beams line and the impact parameter is characterized by the Euler angles. We study the dependences of the HEE and its den…
The entropic approach to dissociation of bound states immersed in strongly coupled systems is developed. In such systems, the excitations of the bound state are often delocalized and characterized by a large entropy, so that the bound state is strongly entangled with the rest of the statistical system. If this entropy $S$ increases with the separation $r$ between the constituents of the bound state, $S = S(r)$, then the resulting entropic force $F = T\ {\partial S}/{\partial r}$ ($T$ is temperature) can drive the dissociation process. As a specific example, we consider the case of heavy quarko…
We study the thermodynamics of the hard wall model, which consists in the introduction of an infrared cut-off in asymptotically AdS spaces. This is a toy model for confining backgrounds in the context of the gauge/gravity correspondence. We use holographic renormalization and reproduce the existence of a Hawking Page phase transition recently discussed by Herzog. We also show that the entropy jumps from $N^0$ to $N^2$, which reinforces the interpretation of this transition as the gravity dual of confinement/deconfinement. We also show that similar results hold for the phenomenologically motiva…
From the viewpoint of holography, we study the behaviors of the entanglement entropy in insulator/superconductor transition with exponential nonlinear electrodynamics (ENE). We find that the entanglement entropy is a good probe to the properties of the holographic phase transition. Both in the half space and the belt space, the non-monotonic behavior of the entanglement entropy in superconducting phase versus the chemical potential is general in this model. Furthermore, the behavior of the entanglement entropy for the strip geometry shows that the confinement/deconfinement phase transition app…
A holographic computation of $T_c$ at ${\it intermediate\ coupling}$ from M-theory dual of thermal QCD-like theories, has been missing in the literature. Filling this gap, we demonstrate a novel UV-IR mixing, (conjecture and provide evidence for) a non-renormalization beyond 1 loop of ${\bf M}-{\bf c}$hiral perturbation theory arXiv:2011.04660[hep-th]-compatible deconfinement ${\bf T}$emperature, and show equivalence with an ${\bf E}$ntanglement (as well as Wald) entropy arXiv:0709.2140[hep-th] computation, up to terms ${\bf Q}$uartic in curvature. We demonstrate a ${\bf F}$lavor-${\bf M}$emor…
We present numerical evidence for a transition between the Klebanov-Strassler background and a solution describing a black hole in the class of cascading solutions in the chirally restored phase. We also present a number of properties of this solution, including the running of the coupling constant, the viscosity to entropy ratio and the drag force on a quark moving in this background.
We continue the study of a recently constructed holographic QCD model supplemented with magnetic field. We consider the holographic dual of a quark, anti-quark pair and investigate its entropy beyond the deconfinement phase transition in terms of interquark distance, temperature and magnetic field. We obtain a clear magnetic field dependence in the strongly decreasing entropy near deconfinement and in the entropy variation for growing interquark separation. We uncover various supporting evidences for inverse magnetic catalysis. The emergent entropic force is found to become stronger with magne…
The $\mathbb{C}P^{N-1}$ sigma model at finite temperature is studied using lattice Monte Carlo simulations on $S_{s}^{1} \times S_τ^{1}$ with radii $L_{s}$ and $L_τ$, respectively, where the ratio of the circumferences is taken to be sufficiently large ($L_{s}/L_τ \gg 1$) to simulate the model on $\mathbb{R} \times S^1$. We show that the expectation value of the Polyakov loop undergoes a deconfinement crossover as $L_τ$ is decreased, where the peak of the associated susceptibility gets sharper for larger $N$. We find that the global PSU($N$)=SU($N$)$/{\mathbb Z}_{N}$ symmetry remains unbroken …
Based on gauge-gravity duality, by using holographic entanglement entropy, we have done a phenomenological study to probe confinement-deconfinement phase transition in the QCD-like gauge theory. Our outcomes are in perfect agreement with the expected results, qualitatively and quantitatively. We find out that the (holographic) entanglement entropy is a reliable order parameter for probing the phase transition.
An interesting case of string/black hole transition occurs in two-dimensional non-critical string theory dressed with a compact CFT. In these models the high energy densities of states of perturbative strings and black holes have the same leading behavior when the Hawking temperature of the black hole is equal to the Hagedorn temperature of perturbative strings. We compare the first subleading terms in the black hole and closed string entropies in this setting and argue that the entropy interpolates between these expressions as the energy is varied. We compute the subleading correction to the …
The dynamics of a probe particle or wrapped brane moving in the two-dimensional Rindler space can be described by a time-dependent tachyon field theory. Using knowledge of tachyon condensation, we learn that the infalling brane gets thermalised and produces open string pairs at the Hagedorn temperature when entering into the near-horizon Rindler wedge. It is shown that the Hagedorn temperature of the infalling brane is equal to the Hawking temperature of the host black hole detected in the same time coordinate. The infalling brane will decay completely into closed strings, mainly massive modes…
The peak of the heavy quark pair entropy at the deconfinement transition, observed in lattice QCD, suggests that the transition is effectively driven by the increase of the entropy of bound states. The growth of the entropy with the inter-quark distance leads to the emergent entropic force that induces dissociation of quarkonium states. Since the quark-gluon plasma around the transition point is a strongly coupled system, we use the gauge-gravity duality to study the entropy of heavy quarkonium and the real-time dynamics of its dissociation. In particular, we employ the Improved Holographic QC…
We study the confinement-deconfinement phase transition of pure Yang-Mills theories at finite temperature using a simple massive extension of standard background field methods. We generalize our recent next-to-leading-order perturbative calculation of the Polyakov loop and of the related background field effective potential for the SU(2) theory to any compact and connex Lie group with a simple Lie algebra. We discuss in detail the SU(3) theory, where the two-loop corrections yield improved values for the first-order transition temperature as compared to the one-loop result. We also show that c…
We study the phase transition in the holographic entanglement entropy for various confining models. This transition occurs for the entanglement entropy of a strip at a critical value of the strip width. Our main interest is to examine the critical width for models with several parameters. For these models, the critical width, the glueball mass and the string tension all become functions of these two parameters. Comparing the behavior of the critical width in the entanglement entropy and these other scales, we find that $l_c$ seems to follow closely the deconfinement temperature and the gluebal…
We investigate the behaviors of holographic entanglement entropy for AdS soliton geometries in the presence of higher derivative corrections. We calculate the leading higher derivative corrections for the AdS5 setup in type IIB string and for the AdS4,7 ones in M-theory. We also study the holographic entanglement entropy in Gauss-Bonnet gravity and study how the confinement/deconfinement phase transition observed in AdS solitons is affected by the higher derivative corrections.
We investigate the behavior of the entanglement entropy of a confining gauge theory near cosmological singularities using gauge/gravity duality. As expected, the coefficients of the UV divergent terms are given by simple geometric properties of the entangling surface in the time-dependent background. The finite (universal) part of the entanglement entropy either grows without bound or remains bounded depending on the nature of the singularity and entangling region. We also discuss a confinement/deconfinement phase transition as signaled by the entanglement entropy.
We study the behaviors of entanglement entropy and vacuum expectation value of Wilson loop in the Stückelberg holographic insulator/superconductor model. This model has rich phase structures depending on model parameters. Both the entanglement entropy for a strip geometry and the heavy quark potential from the Wilson loop show that there exists a "confinement/deconfinement" phase transition. In addition, we find that the non-monotonic behavior of the entanglement entropy with respect to chemical potential is universal in this model. The pseudo potential from the spatial Wilson loop also has a …
In this article, we review recent progresses on the holographic understandings of the entanglement entropy in the AdS/CFT correspondence. After reviewing the general idea of holographic entanglement entropy, we will explain its applications to confinement/deconfinement phase transitions, black hole entropy and covariant formulation of holography.
By constructing the configuration of D3-branes with D(-1)-branes as D-instantons, we study the three-dimensional Yang-Mills Chern-Simons theory in holography. Due to the presence of the D-instantons, the D7-branes with discrepant embedding functions are able to be introduced in order to include the fundamental fermions (as flavors) and the Chern-Simons term (at very low energy) in the dual theory. The vacuum structure at zero temperature is studied in the soliton background and it illustrates the topological phase transition in the presence of instantons. Moreover, since the confinement/deconf…
We investigate the entanglement entropy in gravity duals of confining large $N_c$ gauge theories using the proposal of arXiv:hep-th/0603001, arXiv:hep-th/0605073. Dividing one of the directions of space into a line segment of length $l$ and its complement, the entanglement entropy between the two subspaces is given by the classical action of the minimal bulk hypersurface which approaches the endpoints of the line segment at the boundary. We find that in confining backgrounds there are generally two such surfaces. One consists of two disconnected components localized at the endpoints of the lin…
We investigate the holographic entanglement entropy in the insulator/superconductor phase transition for the Born-Infeld electrodynamics with full backreaction in five-dimensional AdS soliton spacetime. We note that the holographic entanglement entropy is a good probe to study the properties of the phase transition, and the Born-Infeld factor $b$ has no effect on the critical chemical potential $μ_c$. We find that both in the half space and the belt one, the non-monotonic behavior of the entanglement entropy versus the chemical potential is a general property, and the entanglement entropy incr…
We study a holographic gauge theory living in the AdS$_4$ space-time at finite temperature. The gravity dual is obtained as a solution of the type IIB superstring theory with two free parameters, which correspond to four dimensional (4D) cosmological constant ($λ$) and the dark radiation ($C$) respectively. The theory studied here is in confining and chiral symmetry broken phase for $λ<0$ and small $C$. When $C$ is increased, the transition to the deconfinement phase has been observed at a finite value of $C/|λ|$. It is shown here that the chiral symmetry is still broken for a finite range of …
It was proposed by Ryu and Takayanagi that the entanglement entropy in conformal field theory (CFT) is related through the AdS/CFT correspondence to the area of a minimal surface in the bulk. We apply this holographic geometrical method of calculating the entanglement entropy to study the vacuum case of a CFT which is holographically dual to empty anti-de Sitter (AdS) spacetime. We present all possible minimal surfaces spanned on one or two spherical boundaries at AdS infinity. We give exact analytical expressions for the regularized areas of these surfaces and identify finite renormalized qua…
